2015 FRM practice exam

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FRM

Practice Exam

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Introduction 1

Reference Table 2

Special instructions 3

2015 FRM Part I Practice Exam Candidate Answer Sheet 5

2015 FRM Part I Practice Exam Questions 7

2015 FRM Part I Practice Exam Answer Sheet/Answers 19

2015 FRM Part I Practice Exam Explanations 21

2015 FRM Part II Practice Exam Candidate Answer Sheet 45

2015 FRM Part II Practice Exam Questions 47

2015 FRM Part II Practice Exam Answer Sheet/Answers 57

2015 FRM Part II Practice Exam Explanations 59 TABLE OF CONTENTS

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The FRM Exam is a practice-oriented examination Its questions

are derived from a combination of theory, as set forth in the

core readings, and “real-world” work experience Candidates

are expected to understand risk management concepts and

approaches and how they would apply to a risk manager’s

day-to-day activities

The FRM Exam is also a comprehensive examination,

testing a risk professional on a number of risk management

concepts and approaches It is very rare that a risk manager

will be faced with an issue that can immediately be slotted

into one category In the real world, a risk manager must be

able to identify any number of risk-related issues and be

able to deal with them eﬀectively

The 2015 FRM Practice Exams I and II have been developed

to aid candidates in their preparation for the FRM Exam in

May and November 2015 These Practice Exams are based

on a sample of questions from the 2011 through 2014 FRM

Exams and are suggestive of the questions that will be in

the 2015 FRM Examination

The 2015 FRM Practice Exam for Part I contains 25

multiple-choice questions and the 2015 FRM Practice Exam

for Part II contains 20 multiple-choice questions Note that

the 2015 FRM Exam Part I will contain 100 multiple-choice

questions and the 2015 FRM Exam Part II will contain

80 multiple-choice questions The Practice Exams were

designed to be shorter to allow candidates to calibrate

their preparedness without being overwhelming

The 2015 FRM Practice Exams do not necessarily cover

all topics to be tested in the 2015 FRM Exam as the material

covered in the 2015 Study Guide may be diﬀerent from

that covered by the 2011 through 2014 Study Guides The

questions selected for inclusion in the Practice Exams were

chosen to be broadly reﬂective of the material assigned for

2015 as well as to represent the style of question that the

FRM Committee considers appropriate based on assigned

Core readings were selected by the FRM Committee

to assist candidates in their review of the subjects covered

by the Exam Questions for the FRM Exam are derivedfrom the “core” readings It is strongly suggested that candidates review these readings in depth prior to sitting for the Exam

Suggested Use of Practice Exams

To maximize the eﬀectiveness of the Practice Exams, dates are encouraged to follow these recommendations:

candi-1 Plan a date and time to take each Practice Exam

Set dates appropriately to give suﬃcient study/ review time for the Practice Exam prior to the actual Exam

2 Simulate the test environment as closely as possible.

• Take each Practice Exam in a quiet place

• Have only the practice exam, candidate answer sheet, calculator, and writing instruments (pencils, erasers) available

• Minimize possible distractions from other people, cell phones and study material

• Allocate 60 minutes for the Practice Exam and set an alarm to alert you when 60 minutes have passed Complete the exam but note the questions answered after the 60 minute mark

• Follow the FRM calculator policy You may only use

a Texas Instruments BA II Plus (including the BA II Plus Professional), Hewlett Packard 12C (including the HP 12C Platinum and the Anniversary Edition), Hewlett Packard 10B II, Hewlett Packard 10B II+ or Hewlett Packard 20B calculator

3 After completing the Practice Exam,

• Calculate your score by comparing your answer sheet with the Practice Exam answer key Only

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Reference Table: Let Z be a standard normal random variable.

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Special Instructions and Definitions

1. Unless otherwise indicated, interest rates are assumed to be continuously compounded

2. Unless otherwise indicated, option contracts are assumed to be on one unit of the underlying asset

3. VaR = value-at-risk

4. ES = expected shortfall

5. GARCH = generalized auto-regressive conditional heteroskedasticity

6. CAPM = capital asset pricing model

7. LIBOR = London interbank oﬀer rate

8. EWMA = exponentially weighted moving average

9. CDS = credit default swap (s)

10 MBS = mortgage-backed security (securities)

11. CEO/CFO/CRO = Senior management positions: Chief Executive Oﬃcer, Chief Financial Oﬃcer,

and Chief Risk Oﬃcer, respectively

12 The following acronyms are used for selected currencies:

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Practice Exam Part I

Answer Sheet

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Questions

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1. A risk manager performs an ordinary least squares (OLS) regression to estimate the sensitivity of a stock'sreturn to the return on the S&P 500 This OLS procedure is designed to:

a. Minimize the square of the sum of differences between the actual and estimated S&P 500 returns

b. Minimize the square of the sum of differences between the actual and estimated stock returns

c. Minimize the sum of differences between the actual and estimated squared S&P 500 returns

d. Minimize the sum of squared differences between the actual and estimated stock returns

2. Using the prior 12 monthly returns, an analyst estimates the mean monthly return of stock XYZ to be -0.75%with a standard error of 2.70%

ONE-TAILED T-DISTRIBUTION TABLE

Annual Savings = 0.24 * Household Income - 25.66, R² = 0.50

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4. A risk analyst is estimating the variance of stock returns on day n, given by , using the equation

where and represent the return and volatility on day n-1, respectively

If the values of α and β are as indicated below, which combination of values indicates that the variance follows a stable GARCH (1,1) process?

a. α = 0.084427 and β = 0.909073

b. α = 0.084427 and β = 0.925573

c. α = 0.084427 and β = 0.925573

d. α = 0.090927 and β = 0.925573

The following information applies to questions 5 and 6.

A portfolio manager holds three bonds in one of his portfolios and each bond has a 1-year default probability of15% The event of default for each of the bonds is independent

5. What is the probability of exactly two bonds defaulting over the next year?

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7. A risk manager is evaluating a portfolio of equities with an annual volatility of 12.1% per year that is marked to the Straits Times Index If the risk-free rate is 2.5% per year, based on the regression results given inthe chart below, what is the Jensen's alpha of the portfolio?

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9. A risk analyst is reconciling customer account data held in two separate databases and wants to ensure theaccount number for each customer is the same in each database Which dimension of data quality would she

be most concerned with in making this comparison?

a. The delta normal approach

b. The exponentially weighted moving average approach

c. The multivariate density estimation approach

d. The generalized autoregressive conditional heteroskedasticity approach

11. A non-dividend-paying stock is currently trading at USD 40 and has an expected return of 12% per year Usingthe Black-Scholes-Merton (BSM) model, a 1-year, European-style call option on the stock is valued at USD 1.78.The parameters used in the model are:

N(d1) = 0.29123 N(d2) = 0.20333

The next day, the company announces that it will pay a dividend of USD 0.5 per share to holders of the stock

on an ex-dividend date 1 month from now and has no further dividend payout plans for at least 1 year This new information does not affect the current stock price, but the BSM model inputs change, so that:

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12. An at-the-money European call option on the DJ EURO STOXX 50 index with a strike of 2200 and maturing in

1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point The risk-free rate

is 3% per year, and the daily volatility of the index is 2.05% If we assume that the expected return on the DJEURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call option calculated using thedelta-normal approach is closest to:

if the stock price falls by USD 1?

B Decrease by USD 0.94 Increase by USD 0.89

C Decrease by USD 0.07 Increase by USD 0.89

a. Scenario A

b. Scenario B

c. Scenario C

d. Scenario D

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14. Below is a chart showing the term structure of risk-free spot rates:

Which of the following charts presents the correct derived forward rate curve?

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15. A hedge fund manager wants to change her interest rate exposure by investing in fixed-income securities with negative duration Which of the following securities should she buy?

a. Short maturity calls on zero-coupon bonds with long maturity

b. Short maturity puts on interest-only strips from long maturity conforming mortgages

c. Short maturity puts on zero-coupon bonds with long maturity

d. Short maturity calls on principal-only strips from long maturity conforming mortgages

16. A risk analyst is analyzing several indicators for a group of countries If he specifically considers the Gini coefficient in his analysis, in which of the following factors is he most interested?

a. Standard of living

b. Peacefulness

c. Perceived corruption

d. Income inequality

17. A trader writes the following 1-year European-style barrier options as protection against large movements in

a non-dividend paying stock that is currently trading at EUR 40.96

Up-and-in barrier call, with barrier at EUR 45 3.52

Up-and-out barrier call, with barrier at EUR 45 1.24

Down-and-in barrier put, with barrier at EUR 35 2.00

Down-and-out barrier put, with barrier at EUR 35 1.01

All of the options have the same strike price Assuming the risk-free rate is 2% per annum, what is the

common strike price of these options?

a. EUR 39.00

b. EUR 40.00

c. EUR 41.00

d. EUR 42.00

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18. A fixed-income portfolio manager purchases a seasoned 5.5% agency mortgage-backed security with aweighted average loan age of 60 months The current balance on the loans is USD 20 million, and the condi-tional prepayment rate is assumed to be constant at 0.4% per year Which of the following is closest to theexpected principal prepayment this month?

a. AA/Aa

b. A/A

c. BBB/Baa

d. BB/Ba

20. A French bank enters into a 6-month forward contract with an importer to sell GBP 40 million in 6 months at

a rate of EUR 0.80 per GBP If in 6 months the exchange rate is EUR 0.85 per GBP, what is the payoff for thebank from the forward contract?

a. EUR -2,941,176

b. EUR -2,000,000

c. EUR 2,000,000

d. EUR 2,941,176

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21. An oil driller recently issued USD 250 million of fixed-rate debt at 4.0% per annum to help fund a new project

It now wants to convert this debt to a floating-rate obligation using a swap A swap desk analyst for a large investment bank that is a market maker in swaps has identified four firms interested in swapping their debt from floating-rate to fixed-rate The following table quotes available loan rates for the oil driller and each firm:

A swap between the oil driller and which firm offers the greatest possible combined benefit?

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23. A growing regional bank has added a risk committee to its board One of the first recommendations of therisk committee is that the bank should develop a risk appetite statement What best represents a primaryfunction of a risk appetite statement?

a. To quantify the level of variability for each risk metric that a firm is willing to accept

b. To state specific new business opportunities that a firm is willing to pursue

c. To assign risk management responsibilities to specific internal staff members

d. To state a broad level of acceptable risk to guide the allocation of the firm’s resources

24. A German housing corporation needs to hedge against rising interest rates It has chosen to use futures on 10-year German government bonds Which position in the futures should the corporation take, and why?

a. Take a long position in the futures because rising interest rates lead to rising futures prices

b. Take a short position in the futures because rising interest rates lead to rising futures prices

c. Take a short position in the futures because rising interest rates lead to declining futures prices

d. Take a long position in the futures because rising interest rates lead to declining futures prices

25. Barings was forced to declare bankruptcy after reporting over USD 1 billion in unauthorized trading losses by

a single trader, Nick Leeson Which of the following statements concerning the collapse of Barings is correct?

a. Leeson avoided reporting the unauthorized trades by convincing the head of his back office that they did not need to be reported

b. Management failed to investigate high levels of reported profits even though they were associated with a low-risk trading strategy

c. Leeson traded primarily in OTC foreign currency swaps which allowed Barings to delay cash payments on losing trades until the first payment was due

d. The loss at Barings was detected when several customers complained of losses on trades that were booked to their accounts

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Answers

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Explanations

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1. A risk manager performs an ordinary least squares (OLS) regression to estimate the sensitivity of a stock'sreturn to the return on the S&P 500 This OLS procedure is designed to:

a. Minimize the square of the sum of differences between the actual and estimated S&P 500 returns

b. Minimize the square of the sum of differences between the actual and estimated stock returns

c. Minimize the sum of differences between the actual and estimated squared S&P 500 returns

d. Minimize the sum of squared differences between the actual and estimated stock returns

Correct Answer: d

Rationale: The OLS procedure is a method for estimating the unknown parameters in a linear regression model

The method minimizes the sum of squared differences between the actual, observed, returns and the returns estimated by the linear approximation The smaller the sum of the squared differences between observed and estimated values, the better the estimated regression line fits the observed data points

Section: Quantitative Analysis

Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education,

2008) Chapter 4, “Linear Regression with One Regressor.”

Learning Objective: Define an ordinary least squares (OLS) regression and calculate the intercept and slope of the

regression

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2. Using the prior 12 monthly returns, an analyst estimates the mean monthly return of stock XYZ to be -0.75%with a standard error of 2.70%

ONE-TAILED T-DISTRIBUTION TABLE

Rationale: The confidence interval is equal to the mean monthly return plus or minus the t-statistic times the

stan-dard error To get the proper t-statistic, the 0.025 column must be used since this is a two-tailed interval Since themean return is being estimated using the sample observations, the appropriate degrees of freedom to use is equal

to the number of sample observations minus 1 Therefore we must use 11 degrees of freedom and therefore theproper statistic to use from the t-distribution is 2.201

The proper confidence interval is: -0.75% +/- (2.201 * 2.70%) or -6.69% to +5.19%

Reference: Michael Miller, Mathematics and Statistics for Financial Risk Management, 2nd Edition (Hoboken, NJ:

John Wiley & Sons, 2013) Chapter 7, “Hypothesis Testing and Confidence Intervals.”

Learning Objective: Construct and interpret a confidence interval.

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3. Using data from a pool of mortgage borrowers, a credit risk analyst performed an ordinary least squaresregression of annual savings (in GBP) against annual household income (in GBP) and obtained the followingrelationship:

Annual Savings = 0.24 * Household Income - 25.66, R² = 0.50

Assuming that all coefficients are statistically significant, which interpretation of this result is correct?

a. For this sample data, the average error term is GBP -25.66

b. For a household with no income, annual savings is GBP 0

c. For an increase of GBP 1,000 in income, expected annual savings will increase by GBP 240

d. For a decrease of GBP 2,000 in income, expected annual savings will increase by GBP 480

Correct Answer: c

Rationale: An estimated coefficient of 0.24 from a linear regression indicates a positive relationship between

income and savings, and more specifically means that a one unit increase in the independent variable (householdincome) implies a 0.24 unit increase in the dependent variable (annual savings) Given the equation provided, ahousehold with no income would be expected to have negative annual savings of GBP 25.66 The error term mean

is assumed to be equal to 0

Reference: James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education,

2008), Chapter 4, “Linear Regression with One Regressor.”

Learning Objective: Interpret a population regression function, regression coefficients, parameters, slope, intercept,

and the error term.

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4. A risk analyst is estimating the variance of stock returns on day n, given by , using the equation

where and represent the return and volatility on day n-1, respectively

If the values of α and β are as indicated below, which combination of values indicates that the variance follows a stable GARCH (1,1) process?

Rationale: For a GARCH (1,1) process to be stable, the sum of parameters α and β need to be below 1.0

Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson Prentice Hall, 2014),

chapter 23, “Estimating Volatilities and Correlations for Risk Management.”

Learning Objective: Describe the generalized auto regressive conditional heteroskedasticity (GARCH(p,q)) model

for estimating volatility and its properties:

• Calculate volatility using the GARCH(1,1) model

• Explain mean reversion and how it is captured in the GARCH (1,1) model

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The following information applies to questions 5 and 6.

A portfolio manager holds three bonds in one of his portfolios and each bond has a 1-year default probability of15% The event of default for each of the bonds is independent

5. What is the probability of exactly two bonds defaulting over the next year?

Rationale: Since the bond defaults are independent and identically distributed Bernoulli random variables, the

Binomial distribution can be used to calculate the probability of exactly two bonds defaulting

The correct formula to use is =

Where n = the number of bonds in the portfolio, p = the probability of default of each individual bond, and k = thenumber of defaults for which you would like to find the probability In this case n = 3, p = 0.15, and k = 2

Entering the variables into the equation, this simplifies to 3 x 0.152x 0.85 = 0574

John Wiley & Sons, 2013) Chapter 4, “Distributions.”

Learning Objective: Distinguish the key properties among the following distributions: uniform distribution, Bernoulli

distribution, Binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared tribution, Student’s t, and F-distributions, and identify common occurrences of each distribution

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dis-6. What is the mean and variance of the number of bonds defaulting over the next year?

Rationale: Letting n equal the number of bonds in the portfolio and p equal the individual default probability, the

formulas to use are as follows:

Mean = n x p = 3 x 15% = 0.45 Variance = n x p x (1-p) = 3 x 15 x 85 = 0.3825

John Wiley & Sons, 2013), Chapter 4, “Distributions.”

Learning Objective: Distinguish the key properties among the following distributions: uniform distribution, Bernoulli

distribution, Binomial distribution, Poisson distribution, normal distribution, lognormal distribution, Chi-squared distribution, Student’s t, and F-distributions, and identify common occurrences of each distribution

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7. A risk manager is evaluating a portfolio of equities with an annual volatility of 12.1% per year that is marked to the Straits Times Index If the risk-free rate is 2.5% per year, based on the regression results given inthe chart below, what is the Jensen's alpha of the portfolio?

Rationale: The correct answer is d The Jensen's alpha is equal to the y-intercept, or the excess return of the

portfo-lio when the excess market return is zero Therefore it is 3.7069%

Section: Foundations of Risk Management

Reference: Noel Amenc and Veronique Le Sourd, Portfolio Theory and Performance Analysis (West Sussex, England:

John Wiley & Sons, 2003) Chapter 4, Section 4.2 only—”Applying the CAPM to Performance Measurement: Index Performance Measurement Indicators.”

Single-Learning Objective: Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen's alpha.

y = 0.4936x + 3.7069

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8. An investment advisor is analyzing the range of potential expected returns of a new fund designed to cate the directional moves of the BSE Sensex Index but with twice the volatility of the index The Sensex has

repli-an expected repli-annual return of 12.3% repli-and volatility of 19.0%, repli-and the risk free rate is 2.5% per year Assumingthe correlation between the fund’s returns and that of the index is 1, what is the expected return of the fundusing the capital asset pricing model?

Section: Foundations of Risk Management

Reference: Edwin J Elton, Martin J Gruber, Stephen J Brown and William N Goetzmann, Modern Portfolio Theory

and Investment Analysis, 9th Edition (Hoboken, NJ: John Wiley & Sons, 2014) Chapter 13, “The Standard Capital

Asset Pricing Model.”

Learning Objective: Apply the CAPM in calculating the expected return on an asset.

9. A risk analyst is reconciling customer account data held in two separate databases and wants to ensure theaccount number for each customer is the same in each database Which dimension of data quality would she

be most concerned with in making this comparison?

Reference: Anthony Tarantino and Deborah Cernauskas, Risk Management in Finance: Six Sigma and Other Next

Generation Techniques (Hoboken, NJ: John Wiley & Sons, 2009) Chapter 3, “Information Risk and Data Quality

Management.”

Learning Objective: Identify some key dimensions of data quality.

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10. The hybrid approach for estimating VaR is the combination of a parametric and a nonparametric approach Itspecifically combines the historical simulation approach with:

a. The delta normal approach

b. The exponentially weighted moving average approach

c. The multivariate density estimation approach

d. The generalized autoregressive conditional heteroskedasticity approach

Correct Answer: b

Rationale: The hybrid approach combines two approaches to estimating VaR, the historical simulation and the

exponential smoothing approach (i.e an EWMA approach) Similar to a historical simulation approach, the hybridapproach estimates the percentiles of the return directly, but it also uses exponentially declining weights on pastdata similar to the exponentially weighted moving average approach

Section: Valuation and Risk Models

Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational

Risk: The Value at Risk Approach, Chapter 2, “Quantifying Volatility in VaR Models.”

Learning Objective: Compare and contrast different parametric and non-parametric approaches for estimating

conditional volatility

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11. A non-dividend-paying stock is currently trading at USD 40 and has an expected return of 12% per year Usingthe Black-Scholes-Merton (BSM) model, a 1-year, European-style call option on the stock is valued at USD 1.78.The parameters used in the model are:

N(d1) = 0.29123 N(d2) = 0.20333

The next day, the company announces that it will pay a dividend of USD 0.5 per share to holders of the stock

on an ex-dividend date 1 month from now and has no further dividend payout plans for at least 1 year This new information does not affect the current stock price, but the BSM model inputs change, so that:

Rationale: The value of a European call is equal to S * N(d1) – Ke-rT* N(d2), where S is the current price of the stock

In the case that dividends are introduced, S in the formula is reduced by the present value of the dividends

Furthermore, the announcement would affect the values of S, d1and d2 However, since we are given the new values, and d2is the same, the change in the price of the call is only dependent on the term S * N(d1)

Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, Chapter 15, “The Black-Scholes-Merton

Model.”

Learning Objective: Compute the value of a European option using the Black-Scholes-Merton model on a

dividend-paying stock

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12. An at-the-money European call option on the DJ EURO STOXX 50 index with a strike of 2200 and maturing in

1 year is trading at EUR 350, where contract value is determined by EUR 10 per index point The risk-free rate

is 3% per year, and the daily volatility of the index is 2.05% If we assume that the expected return on the DJEURO STOXX 50 is 0%, the 99% 1-day VaR of a short position on a single call option calculated using thedelta-normal approach is closest to:

Rationale: Since the option is at-the-money, the delta is close to 0.5 Therefore a 1 point change in the index would

translate to approximately 0.5 * EUR 10 = EUR 5 change in the call value

Therefore, the percent delta, also known as the local delta, defined as %D = (5/350) / (1/2200) = 31.4

So the 99% VaR of the call option = %D * VaR(99% of index) = %D * call price * alpha (99%) * 1-day volatility = 31.4 *EUR 350 * 2.33 * 2.05% = EUR 525 The term alpha (99%) denotes the 99th percentile of a standard normal

distribution, which equals 2.33

There is a second way to compute the VaR If we just use a conversion factor of EUR 10 on the index, then we canuse the standard delta, instead of the percent delta:

VaR(99% of Call) = D * index price * conversion * alpha (99%) * 1-day volatility = 0.5 * 2200 * 10 * 2.33 * 2.05% = EUR 525, with some slight difference in rounding

Both methods yield the same result

Reference: Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational

Risk: The Value at Risk Approach, Chapter 3, “Putting VaR to Work.”

Learning Objective: Compare delta-normal and full revaluation approaches for computing VaR.

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13. The current stock price of a company is USD 80 A risk manager is monitoring call and put options on thestock with exercise prices of USD 50 and 5 days to maturity Which of these scenarios is most likely to occur

if the stock price falls by USD 1?

B Decrease by USD 0.94 Increase by USD 0.89

C Decrease by USD 0.07 Increase by USD 0.89

Rationale: The call option is deep in-the-money and must have a delta close to one The put option is deep

out-of-the-money and will have a delta close to zero Therefore, the value of the in-out-of-the-money call will decrease by close

to USD 1, and the value of the out-of-the-money put will increase by a much smaller amount close to 0 The choicethat is closest to satisfying both conditions is A

Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, Chapter 19, “The Greek Letters.”

Learning Objective: Describe the dynamic aspects of delta hedging.

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14. Below is a chart showing the term structure of risk-free spot rates:

Which of the following charts presents the correct derived forward rate curve?

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15. A hedge fund manager wants to change her interest rate exposure by investing in fixed-income securities with negative duration Which of the following securities should she buy?

a. Short maturity calls on zero-coupon bonds with long maturity

b. Short maturity puts on interest-only strips from long maturity conforming mortgages

c. Short maturity puts on zero-coupon bonds with long maturity

d. Short maturity calls on principal-only strips from long maturity conforming mortgages

Correct Answer: c

Rationale: In order to change her interest rate exposure by acquiring securities with negative duration, the manager

will need to invest in securities that decrease in value as interest rates fall (and increase in value as interest ratesrise) Zero coupon bonds with long maturity will increase in value as interest rates fall, so calls on these bonds willincrease in value as rates fall but puts on these bonds will decrease in value and this makes C the correct choice.Interest-only strips from long maturity conforming mortgages will decrease in value as interest rates fall, so puts onthem will increase in value, while principal strips on these same mortgages will increase in value, so calls on themwill also increase in value

Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 4, “One-Factor Risk Metrics and Hedges.”

Learning Objective: Define, compute and interpret the effective duration of a fixed income security given a change

in yield and the resulting change in price

Section: Financial Markets and Products

Reference: Bruce Tuckman, Fixed Income Securities, 3rd Edition, Chapter 20, "Mortgages and Mortgage-Backed

Securities."

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16. A risk analyst is analyzing several indicators for a group of countries If he specifically considers the Gini coefficient in his analysis, in which of the following factors is he most interested?

Rationale: The Gini coefficient is commonly used to measure income inequality on a scale of zero to one, with zero

being total equality and one being total inequality Therefore, nations with lower Gini coefficients have a more evendistribution of income, while higher Gini coefficients indicate a wider disparity between higher and lower incomehouseholds

Reference: Daniel Wagner, Managing Country Risk: A Practitioner’s Guide to Effective Cross-Border Risk Analysis,

chapter 4, “Country Risk Assessment in Practice.”

Learning Objective: Describe alternative measures and indices that can be useful in assessing country risk.

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17. A trader writes the following 1-year European-style barrier options as protection against large movements in

a non-dividend paying stock that is currently trading at EUR 40.96

Up-and-in barrier call, with barrier at EUR 45 3.52

Up-and-out barrier call, with barrier at EUR 45 1.24

Down-and-in barrier put, with barrier at EUR 35 2.00

Down-and-out barrier put, with barrier at EUR 35 1.01

All of the options have the same strike price Assuming the risk-free rate is 2% per annum, what is the

common strike price of these options?

Rationale: The sum of the price of an up-and-in barrier call and an up-and-out barrier call is the price of an

other-wise equivalent European call The price of the European call is EUR 3.52 + EUR 1.24 = EUR 4.76

The sum of the price of a down-and-in barrier put and a down-and-out barrier put is the price of an otherwise equivalent European put The price of the European put is EUR 2.00 + EUR 1.01 = EUR 3.01

Using put-call parity, where C represents the price of a call option and P the price of a put option,

C + Ke-r= P + S

K = er(P + S – C)

Hence, K = e0.02* (3.01 + 40.96 – 4.76) = 40.00

Section: Financial Markets and Products

Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition, chapter 26, “Exotic Options.”

Learning Objective: Identify and describe the characteristics and pay-off structure of the following exotic options:

Chooser and barrier options

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